The Cosmochrony Research Programme: A Structural Roadmap and Paper Inventory

The Cosmochrony programme develops a pre-geometric framework in which physical structure — spacetime, quantum mechanics, gauge symmetry, and Standard Model observables — arises from a single primitive: the local structure of admissible non-injective transitions between observable states. The corpus comprises 71 papers across three theory branches. Branch I (Foundation track) builds the axiomatic base: four axioms suffice to derive the Heisenberg group Heis₃ (Z/qZ) and its Weil representation as theorems, without any background substrate or relaxation mechanism. Branch II (O-series) develops the spectral admissibility sub-programme, deriving and numerically validating the transfer chain c_ ₏₀₈ₑ ^* 0. 126 connecting the BI saturation constant to the charged-lepton mass hierarchy. Branch III (Q-series and companion papers) derives quantum mechanics, spacetime geometry, gauge structure, and further physical observables from Branch I axioms and Branch II spectral data. Paper Q3 completes the SU (2) quantum sector: by combining BI indiscernibility with Schur's lemma on the Clebsch–Gordan decomposition of ₂₉+₁₂₉+₁, the universal singlet correlator E (a, b) = -j (j+1) /3 (a) and the Born rule are derived for all five admissible sectors of 2I, closing the general-j extension that was open in Q2. The geometric emergence sub-programme (Q5a–Q10, U1, W1, H2) closes the effective spacetime identification: under the Q5a continuum-limit hypotheses, the lifting hypothesis H-lift is proved (Q9), asymptotic su (2) -isotropy AH 2 is proved (Q10, U1), the admissibility weight convergence H-w is proved (W1), yielding the effective Lorentzian co-metric g^ = diag (-2, 2, 2, 2) ^ (A_ = 2, Q11). Q5a v2. 0 establishes that H1 is not needed in full generality. Q5a-O2 proves spectral atomicity of the admissible sector (each pair spans three pure Fourier modes) and closes hypotheses H-E1 and C without Nash inequalities. Hypothesis H2 (strong convergence of the rescaled Weil generators) is proved (H2 paper), closing all hypotheses of the Q5a large-q convergence theorem unconditionally on the admissible sector. O31 develops the structural framework for the SU (3) identification: the metaplectic intertwining of Heis₃ (Z/qZ) forces triplet co-admissibility unconditionally for the colour-adapted Cayley graph, and SU (3) is thereby identified as the symmetry group of the co-admissible colour triplet conditional on H-color. This paper provides a complete inventory, a logical dependency map, and a structured account of what is proved, structural, heuristic, or open. It is intended both as an entry point for external readers and as an internal navigation reference.